Question: Simplify the following expression: $z = \dfrac{1}{5q} + \dfrac{1}{10q}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5q$ and $10q$ $\lcm(5q, 10q) = 10q$ $ z = \dfrac{2}{2} \cdot \dfrac{1}{5q} + \dfrac{1}{1} \cdot \dfrac{1}{10q} $ $z = \dfrac{2}{10q} + \dfrac{1}{10q}$ $z = \dfrac{2 +1}{10q}$ $z = \dfrac{3}{10q}$